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arXiv · 2304.12022

A type $B$ analog of Ish arrangement

Tan Nhat Tran·Shuhei Tsujie
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Abstract

The Shi arrangement due to Shi (1986) and the Ish arrangement due to Armstrong (2013) are deformations of the type $A$ Coxeter arrangement that share many common properties. Motivated by a question of Armstrong and Rhoades since 2012 to seek for Ish arrangements of other types, in this paper we introduce an Ish arrangement of type $B$. We study this Ish arrangement through various aspects similar to as known in type $A$ with a main emphasis on freeness and supersolvability. Our method is based on the concept of $ψ$-digraphic arrangements recently introduced due to Abe and the authors with a type $B$ extension.

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Tan Nhat Tran, Shuhei Tsujie. 2023-04-24. A type $B$ analog of Ish arrangement. https://arxiv.org/abs/2304.12022

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